Coverage control is one area of multi-robot or multi-agent control that has received significant attentions. Coverage control is concerned with how to position robots in such a way that “surveillance” of a domain of interest is maximized, where areas of importance within the domain of interest are associated with a density function. The focus of existing coverage algorithms have largely been on static density functions, which does not provide a flexible solution for a dynamically changing environment, for example, when the areas of importance within the domain of interest change. Also, in the existing coverage algorithms, each robot knows the positions of all robots in the multi-robot system. As a result, the existing system may be prone to crash when handling a large number of robots.
To date, relatively little work has been done on coverage with time-varying density functions. In J. Cortes, S. Martinez, T. Karatas, and F. Bullo, “Coverage control for mobile sensing networks: Variations on a theme,” in Mediterranean Conference on Control and Automation, Lisbon, Portugal, 2002, Electronic Proceedings, the time-varying case was investigated under a set of simplifying assumptions on the density functions. However, those assumptions do not hold in general and their violations may even cause the algorithm to break down. Another stab at the problem was pursued in L. C. A. Pimenta, M. Schwager, Q. Lindsey, V. Kumar, D. Rus, R. C. Mesquita, and G. A. S. Pereira, “Simultaneous coverage and tracking (scat) of moving targets with robot networks.” in WAFR, ser. Springer Tracts in Advanced Robotics, vol. 57. Springer, 2008, pp. 85-99, where time-varying density functions were used as a means to track moving targets. However, formal guarantee of achieving coverage were absent from these existing attempts.
There is a need for a reliable, robust and flexible solution with optimal coverage when human operators wish to adaptively interact with a team of robots through a dynamic re-shaping of the density functions. There is also a need for an optimal control solution for a multi-robot switched autonomous system.